Chiral Spin Liquids at Finite Temperature in a Three-Dimensional Kitaev Model

Abstract: Chiral spin liquids (CSLs) in three dimensions and thermal phase transitions to paramagnet are studied by unbiased Monte Carlo simulations. For an extension of the Kitaev model to a three-dimensional tricoordinate network dubbed the hypernonagon lattice, we derive low-energy effective models in two different anisotropic limits. We show that the effective interactions between the emergent $Z_2$ degrees of freedom called fluxes are unfrustrated in one limit, while highly frustrated in the other. In both cases, we find a first-order phase transition to the CSL, where both time-reversal and parity symmetries are spontaneously broken. In the frustrated case, however, the CSL state is highly exotic --- the flux configuration is subextensively degenerate while showing a directional order with broken $C_3$ rotational symmetry. Our results provide two contrasting archetypes of CSLs in three dimensions, both of which allow approximation-free simulation for the thermodynamics.